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We discuss the role of differential rotation in the evolution of the l=2r-mode instability of a newly born, hot, rapidly-rotating neutron star. It isshown that the amplitude of the r-mode saturates in a natural way at a valuethat depends on the amount of differential rotation at the time the instabilitybecomes active. It is also shown that, independently of the saturationamplitude of the mode, the star spins down to a rotation rate that iscomparable to the inferred initial rotation rates of the fastest pulsarsassociated with supernova remnants.Comment: 4 pages, 2 figures, in Proceedings of the 5th International Workshop  "New Worlds in Astroparticle Physics", Faro, Portugal, 8-10 January 200

THE ROLE OF DIFFERENTIAL ROTATION IN THE EVOLUTION OF THE r-MODE INSTABILITY